The cross helicity at the solar surface by simulations and observations

Abstract

The quasilinear mean-field theory for driven MHD turbulence leads to the result that the observed cross helicity <u \cdot b> may directly yield the magnetic eddy diffusivity \eta_{T} of the quiet Sun. In order to model the cross helicity at the solar surface, magnetoconvection under the presence of a vertical large-scale magnetic field is simulated with the nonlinear MHD code NIRVANA. The very robust result of the calculations is that < u_z b_z >\simeq 2 < u\cdot b> independent of the applied magnetic field amplitude. The correlation coefficient for the cross helicity is about 10%. Of similar robustness is the finding that the rms value of the magnetic perturbations exceeds the mean-field amplitude (only) by a factor of five. The characteristic helicity speed u_{\eta} as the ratio of the eddy diffusivity and the density scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s for weak fields. This value well coincides with empirical results obtained from the data of the HINODE satellite and the Swedish 1-m Solar Telescope (SST) providing the cross helicity component < u_z b_z >. Both simulations and observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as characteristic for the surface of the quiet Sun.